User talk:SlamDiego/Archive 10

Marginal utility
On the above article, Slam, I had just completed addressing your (5) on the above Talk page when I discovered your two added comments. The sun may never set on SlamDiego, but it definitely rises for me. And I plan to rise with it. I do not believe that you have addressed my last Edit summary. It is easy to claim correctness if the statement is too obscure to say anything about it. The audience should be not me but the poor but brilliant soul without benefit of much background trying to make sense of the first sentence on the basis of what is there. If you have the itch, hope you have more to say on the above Talk page (on your own schedule of course & not ncessarily soon). But I probably won't be able to respond soon. I know that will disappoint you, but get over it. --Thomasmeeks 01:15, 15 July 2007 (UTC)


 * I'll be glad to respond to any specific assertions or questions that you put on the article talk page. Concerning points actually in contention, I'll be glad to direct you to which of the references already in the article deal with those points.  The reason that there isn't a whole lot there in that first sentence is that a lot less needs to be there than the British marginalists and their neoclassical heirs thought and think.  The extra stuff that they incorporated is discussed in the body of the article. —SlamDiego&#8592;T 01:29, 15 July 2007 (UTC)


 * BTW, I expected my comment
 * This article is laden with references that make plain that the neoclassical conception of utility is a special case.
 * to the talk page to be read in the context of my immediate prior edit summary:
 * It is only a *rate* under the presumption of quantification.
 * —SlamDiego&#8592;T 05:47, 15 July 2007 (UTC)
 * OK, thx. I'm swamped w other stuff now, so it may take time (a week?) to get back. I have something (more than a little), just not complete.   --Thomasmeeks 10:25, 15 July 2007 (UTC)

Digwuren
What do you mean by this and this mysterious comment? What relation to Grazon from California is User:Digwuren from Estonia supposed to have if he is not even mentioned in this checkuser case? Colchicum 12:41, 15 July 2007 (UTC)


 * You are making strange inferential leaps (albeit tentatively). This first edit informed Digwuren of the checkuser because Digwuren has been having trouble with Dcker, who I argued for that RfC is a sockpuppet of  Grazon.  The second edit is simply in response to an amusing passage by Digwuren.  As to the accusations of puppetry against Digwuren which prompted that passage, I am not sufficiently versed in the particulars to form much of an opinion. —SlamDiego&#8592;T 14:00, 15 July 2007 (UTC)
 * Ok then. Thanks for the clarification. Colchicum 14:02, 15 July 2007 (UTC)

User:Dcker
Looks like he's already blocked indef (I was going to go do it myself but someone beat me to it!)...  "Likely" is often the best you'll get out of Checkuser just due to the vagaries of the internet and IP protocol. ---J.S (T/C/WRE) 00:35, 16 July 2007 (UTC)

Questions and comments about marginal utility...
Dear Slam,

It seems we are making some progress on the MU page... there is still a great deal I would change, but I am going to start by asking some questions here before making further adjustments to the text.

You are using a lot of words that are unclear to me. (More precisely, the page uses a lot of words that are unclear to me... but I assume much of it is your writing.) Part of this is definitely due to my ignorance about Austrian interpretations of utility. It could reflect rustiness regarding the neoclassical interpretations too... though hopefully not.


 * I wrote the article without using terminology peculiar to any school or schools or economic thought. The problem, as developed below, is that you have been so sure of some mistaken mathematical assumptions that you've struggled to think outside of the box that they form. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

You say at some point that "an individual will typically be able to partially order the potential uses of a good or service". Am I therefore correct to assume that we are always restricting attention in this page to "ordinal" utility? By ordinal utility, I mean that the person can say "I like consuming 3 bananas and 2 oranges better than consuming 1 banana and 3 apples" for some but not necessarily all pairs of consumption baskets. In other words, having ordinal utility means, to the best of my knowledge, that an individual can rank some but not necessarily all consumption baskets. In order to be a ranking, it must by definition not be cyclical (i.e. I can't like A better than B better than A.) But it's not necessarily complete: I might like A better than B and A better than C, but not know whether I prefer B or C (which is obviously not the same as being indifferent between them).


 * Since writing the above, I've seen some of your other comments on ordinal utility, where you call it "weak cardinal", for example. I guess if "ordinal" means a complete ordering, instead of a partial ordering, then indeed it would always imply a cardinal ordering too (just numbering by rank). But if "ordinal" means a partial ordering, then in general we can't associate it with a cardinal ordering. --Rinconsoleao 22:36, 19 July 2007 (UTC)


 * You are still confused. Indeed, what you call “ordinal” is quantified.  However, your belief that any full ordering will correspond to a measure is false, and I have repeatedly made the point on the article talk page that it is false.  I linked to a free, on-line copy of the article by Kraft &amp;alii which originally provided the mathematics that it false, and referenced the economics article that later applied this to utility.  I have repeatedly made this point.


 * (Partial ordering allows marginal utility to be applied, but only over subsets which are themselves ordered.) —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

When I talk about cardinal utility I mean putting a number on each consumption basket, and ranking consumption baskets according to those numbers. As long as I put a number on every basket, the ordering becomes complete rather than partial. (Again, ranking requires that there are no cycles.) Thus, I think of cardinal utility as a special case of ordinal utility: it does  the ranking by assigning numbers.

It appears to me that when you say "quantified", you mean the same as I mean by "cardinal". Is this correct, or am I missing some subtlety here?


 * You are mistaken, and your revised interpretation is mistaken.
 * The neoclassical conception of “cardinal” utility is one in which measures fit the ordering, and some unique measure says something uniquely meaningful, so that someone with a God's eye view could say things such as “John is twice as happy as Pete.”
 * The neoclassical conception of “ordinal” utility is one in which measures fit, but none is assumed to fit uniquely. This may mean
 * that measures are meaningful up to an affine transformation (confused with the narrower case of linear transformations by Thomasmeeks and others). This would allow God to say such things as “John is twice as happy as he was.” but not to say “John is twice as happy as Peter.”  And EU maximization is conceivable.
 * just that measures are meaningful up to a monotonic transformation. It is still possible then to do some weak arthimetic with utility.
 * Then we have the Mengerian notion, in which no measure is assumed to fit at all. (And, since de Finetti's conjecture was wrong, this notion captures rational orderings excluded by what the neoclassicals call “ordinal”.)
 * Finally, we have partial orderings, under which marginal utility analysis will sometimes be meaningful.
 * —SlamDiego

However, you clearly equate "quantified utility" with utility which is a "measure" (and you link that to measure theory). I always thought of cardinal utility as simply being a ranking done by assigning numbers. I don't recall seeing it pointed out that that this is the same as saying that utility is a "measure", in the sense of measure theory. Is it obvious that this is the same thing?


 * What is obvious differs across persons; it is correct. —SlamDiego

I rather doubt it, because ranking of consumption bundles permits utility to be DECREASED by consuming too much (i.e. marginal utility can be negative); but a measure, by definition, can't be a decreasing function. (Maybe if we rank consumption bundles under the assumption that free disposal is possible, then a utility ranking implies the existence of a measure. But it's not immediately obvious to me.)


 * That confuses an assumption of more being better with an assumption that some measure can be fit to each bundle (whether uniquely or otherwise).


 * The relevant questions is of the relationship of the preference relation to the utility function. If we can map from $$\geqslant$$ on some set of numbers associated with bundles to $$\succcurlyeq$$ on that set of bundles, then we have a measure. (Again, a measure may or may not be unique.) —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)


 * I'm afraid your comment on DeFinetti's conjecture goes straight over my head. I will try to look that up at some point. --Rinconsoleao 22:40, 19 July 2007 (UTC)


 * It's central to the proof that the neoclassical conception is not fully general. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

In one of the revisions you said that my definition, "The MU of a good is the increase in utility obtained by consuming (or using) one more unit of that good or service" applied to ordinal utility in general as well as cardinal utility in particular. But I don't see how that can be the case. If I can only rank goods, but can't give them numbers, then I don't understand what "the increase in utility" means.


 * It means movement from some $$S_n$$ to some $$S_m$$ such that $$S_m~\succ~S_n$$. It means that but not just that in the neoclassical conception; it means just that in the Austrian School conception. —SlamDiego

In fact, the definition you offer (least urgent / best feasible) does not mention an INCREASE in utility associated with the marginal unit. Instead, it seems to refer to the LEVEL of utility associated with that particular allocation.


 * To apply the word “increase” to the Mengerian conception, we must take it to mean improvement, rather than something quantitative. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

Am I missing something here?


 * In some ways, you're almost there. Yeah, a non-quantitative conception won't allow quantitative relations (such as $$\geqslant$$), just as it won't allow quantitative operations.  That's why I carefully eschewed them in the article except in the context of a special case identified as such. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

Maybe the problem is that I am accustomed (by the way I've been taught) to associate utility with consumption BASKETS; and therefore insofar as I associate utility with goods it is only by looking at the "marginal" difference of baskets with and without that good. I.e. for me UTILITY refers to baskets, and MARGINAL UTILITY to goods. When you say "the utility of its least urgent use", does this refer to the utility OF THAT GOOD, or OF THE CONSUMPTION BASKET attained by adding that good?


 * It refers to the good explicitly, but must refer to the state-of-the-world (“basket”) implicitly; and that really also obtains with the neoclassical conception as well, so I didn't see this as the primary issue. But maybe it is primary, in the sense that one must back-up to the level of states-of-the-world when first rethinking things. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

Also, What does "use" mean? At some point you said utility was meant in the sense of "use" (which you italicized, but that's no substitute for explaining what you meant.) You make clear that use is not the same as pleasure. When you say "use", do you simply mean "whatever my goal is", be that pleasure, or success, or some other goal?


 * Before I quite answer that, consider the word “utility”. Its base meaning is use.  The Bethamites associated it with pleasure and with the avoidance of pain, believing that these were the only ultimate uses of things.  So, setting aside whether they were right, in what sense of “use” is this claim meaningful?  That sense is the sense of “use” that applies.


 * So, to explicitly answer your question: The word “use” means application towards a goal. Any application could be said to at least attain a sub-goal, which can itself be called a “goal”.  There are three isomorphisms tying together use, goal, and satisfaction. —SlamDiego

The other reason I still don't fully understand the definition you offered was that you didn't answer my frenchfry question. Was that example a correct interpretation?


 * No. And I did answer implicitly in my more general response. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% A couple of changes I would make:

If "cardinal" is the same as "quantified", I would use the word "cardinal" instead. To the best of my knowledge, "cardinal" is the standard term (and wikip has a page on cardinal utility but not on quantified utility). If "cardinal" is the neoclassical term, and "quantified" is the Austrian or Marxist term or whatever, then we should mention both terms, and state clearly whether or not they are equivalent.


 * It isn't. That's why I have repeatedly said that it isn't. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

In the section on market price, the page says "On the assumption that purchasable goods have DMU, the marginal utility of money will itself be diminishing." This is simply false. If utility is a constant-returns-to-scale Cobb-Douglas function of apples and oranges, then the marginal utility of money will be constant, but there will be DMU in apples by themselves, and there will also be DMU in oranges by themselves.


 * That passage was in fact correct (it didn't begin “On the assumption that each purchasable good has”), but I deleted it because (1) it's not vital, (2) your response made me see that it could easily be misread, and (3) I fear that it would swell monstrously if rewritten to avoid the misreading. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

Actually, adding a short section on the (quite different) roles played by the DMU assumption for individual goods, and the DMU assumption applied to the marginal dollar, could be quite helpful.


 * You may be right. I certainly don't object to the idea. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

--Rinconsoleao 22:31, 19 July 2007 (UTC)


 * Please stop inserting needless newlines in your edits; they make it difficult to respond to your comment, and harder to read the article in source. —SlamDiego&#8592;T 01:55, 20 July 2007 (UTC)

Thanks! All extremely helpful (including your advice on newlines). Over time I will try to clear up some aspects of the text to make them easier to read without losing sight of the points you are making. --Rinconsoleao 08:00, 20 July 2007 (UTC)